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Let $G$ be a simply-connected, simple compact Lie group of type$\{n_{1},\ldots,n_{\ell}\}$, where $n_{1}\le\cdots \le n_{\ell}$. Let$\mathcal{G}_k$ be the gauge group of the principal $G$-bundle(namedright{P}{}{S^{4}}) whose isomorphism class is determined by the thesecond Chern class having value $k\in\mathbb{Z}$. We calculate the mod-$p$homology of the classifying space $B\mathcal{G}_k$ provided that $n_{\ell}<p-1$and $p$ does not divide $k$.

The mod-$p$ homology of the classifying spaces of certain gauge groups